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11.Thermodynamics
hard
During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_p}{C_V}$ for the gas is:
A
$\frac{5}{3}$
B
$\frac{9}{7}$
C
$\frac{3}{2}$
D
$\frac{7}{5}$
(JEE MAIN-2024)
Solution
$\mathrm{P} \propto \mathrm{T}^3$
$\mathrm{PT}^{-3}=\text { constant }$
$\because \frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{nR}=\text { constant from ideal gas equation }$
$(\mathrm{P})(\mathrm{PV})^{-3}=\text { constant }$
$\mathrm{P}^{-2} \mathrm{~V}^{-3}=\text { cosntant } \quad . .(1)$
$\because \text { Process equation for adiabatic process is }$
$\mathrm{PV}^y=\text { constant } \quad . .(2)$
$\text { Comparing equation (1) and (2) }$
$\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{V}}}=\mathrm{y}=\frac{3}{2}$
Standard 11
Physics
